YES

TRS:

  min(X,0()) -> X
  min(s(X),s(Y)) -> min(X,Y)
  quot(0(),s(Y)) -> 0()
  quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
  log(s(0())) -> 0()
  log(s(s(X))) -> s(log(s(quot(X,s(s(0()))))))

max/plus interpretations on N:

  min_A(x1,x2) = max{5, x1, 13}
  min#_A(x1,x2) = max{0, -1, 1}
  0_A = 17
  0#_A = 17
  s_A(x1) = max{30, 11 + x1}
  s#_A(x1) = max{29, 13}
  quot_A(x1,x2) = max{16, x1, 15}
  quot#_A(x1,x2) = max{15, 1 + x1, 14}
  log_A(x1) = max{10, -10 + x1}
  log#_A(x1) = max{0, -12 + x1}

precedence:

  log > quot > min = s > 0